In this paper, we propose and study a risk model with two types of claims in which the insurer may invest into a prevention plan which decreases the large claims intensity without impacting the small claims. In this setting, we prove that prevention is advantageous when claim severities for small and large claims are ordered in the sense of the Harmonic-Mean-Residual-Lifetime (HMRL) order. In addition, we show that the optimal prevention amount is the lowest when there is no initial surplus. Finally, we characterize the asymptotic optimal prevention strategy when the initial surplus tends to infinity in the two main cases where both claim types are light-tailed and where one of them is light-tailed and the other one is heavy-tailed.

中文翻译：

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两种索赔的最佳预防大风险

在本文中，我们提出并研究了一种具有两种类型索赔的风险模型，在该模型中，保险公司可以投资于一种预防计划，该计划可以在不影响小额索赔的情况下降低大额索赔的强度。在这种情况下，我们证明，当根据谐波平均残差寿命 (HMRL) 顺序对小额和大额索赔的索赔严重性进行排序时，预防是有利的。此外，我们表明，当没有初始盈余时，最佳预防量最低。最后，在两种主要情况下，当初始盈余趋于无穷大时，我们描述了渐近最优预防策略，其中两种索赔类型都是轻尾，其中一种是轻尾，另一种是重尾。